Lattice-driven magnetoresistivity and metal-insulator transition in single-layered iridates*

{Sr$_{2}$IrO$_{4}$} exhibits a novel insulating state driven by spin-orbit interactions. Here we report two novel phenomena, namely a large magnetoresistivity that is extremely sensitive to the orientation of magnetic field but exhibits no apparent correlation with the magnetization, and a robust metallic state that is induced by dilute electron {(La$^{3+}$)} or hole (K$^{+}$) doping on Sr$^{2+}$ ions in {Sr$_{2}$IrO$_{4}$}. This study reveals that a strong spin-orbit interaction alters the balance between the competing energies so profoundly that (1) the spin degree of freedom alone is no longer a dominant force; (2) underlying transport properties delicately hinge on the {Ir-O-Ir} bond angle via a strong magnetoelastic coupling; and (3) a highly insulating state in {Sr$_{2}$IrO$_{4}$} is proximate to a metallic state, and the transition is governed by lattice distortions that can be controlled via either magnetic field or chemical doping.